An external point is situated at a distance of 17 cm from the centre of a circle having 16 cm diameter. Determine the length of the tangent drawn to the circle from the external point.

Explanation

Since the diameter of the circle with centre O is 16 cm.
`therefore` radius `=16/2cm =8 cm.`
PT is a tangent to the circle from an external point P which is situated at a distance of 17 cm from the centre of the circel `therefore OP= 17cm.`
We have to determin the length of PT.
Now, PT is a tangent at T to the circle with centre O and OT is the radius passing through point of contact.
`therefore OT bot PT, therefore angle PTO =1` right angle.
So, from the right-angled triangle POT by pythagoras' theorem,
`OP^(2)=OT^(2)+PT^(2)`
`or, 17^(2)=8^(2) +PT^(2) [because OP=17 cm, OT= 8cm]`
Math (X) -22
`or, 289=64+ PT^(2) or, PT^(2)=289-64`
`or PT^(2) =225 or, PT =sqrt225=15.`
`therefore` the required length of the tangent = 15 cm.